Start your tour of Chicago with a sampling of the city's famed architecture. Take a guided walking tour with the Chicago Architecture Foundation. This two hour tour traverses the Loop, giving insight into the city's history and letting you feel the pulse of the city. There is also an architectural boat tour available that runs along the Chicago River and Lake Michigan, if you don't feel like walking.
Next, head to the lakeshore and check out some of the city's excellent museums. The Adler Planetarium, the Field Museum, and the Shedd Aquarium are all located here. It is not possible to do all three justice in one day, so pick whichever two most interest you.
Across the Lake Shore Drive from the museums is Millennium Park. Chicago's newest park is a great place to relax after the walking around museums for a few hours. Sit back, enjoy the skyline, and people watch, or check out the modern art installations. During the summer, free concerts are often held in the Frank Gehry designed Pritzker Music Pavilion.
When you've had enough of the park, take a walk down Michigan Avenue, and soak up what is perhaps the world's most spectacular cityscape. Words don't do the view from over the Chicago River justice. Stop at the John Hancock Building. Take the second fastest elevator in the world to the Observatory, where you can see the amazing panoramic view. On a clear day you can see three states: Indiana, Wisconsin, and Michigan, clear across Lake MIchigan.
Get dinner at one of the many excellent restaurants around the Loop. If you're looking for something a little more exotic, take the El down to Chinatown. Finish your day further north along Michigan Avenue at one of America's best shopping districts.